is my working correct? Vector equations and planes.

is my working correct? Vector equations and planes.

Is my working correct with regards to the following question? Any feedback
is appreciated.
Question: Find a vector equation for the plane that passes through the
points $A(1, 1,a),B(2, 0,−1)$ and $C(−2, 1,−1)$. If a
has the value $−1$, what can you say about the plane?
Is my working correct?
Vector $BA = <-1 , 1, 1+a>$ and vector $CA=<3, 0, 1+a>$
A normal vector to the plane $ABC$ is the vector product
$$n=BA x CA =<1+a, 4(1+a), - 3> $$
A vector equation for the plane is
$$r.n = (2,0,-1).(1+a, 4(1+a), -3) =5+2a$$
If $a=-1$ the plane has equation $r.(0,0,-3) = 3$
which has Cartesian equation $z=-1$ and this is a plane parallel to the
$x-y$ plane.